/*
-----------------------------------------------------------------------------
This source file is part of OGRE
(Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2006 Torus Knot Software Ltd
Also see acknowledgements in Readme.html

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.

This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 59 Temple
Place - Suite 330, Boston, MA 02111-1307, USA, or go to
http://www.gnu.org/copyleft/lesser.txt.

You may alternatively use this source under the terms of a specific version of
the OGRE Unrestricted License provided you have obtained such a license from
Torus Knot Software Ltd.
-----------------------------------------------------------------------------
*/
#ifndef __MATRIX4_H_INCL__
#define __MATRIX4_H_INCL__

#include "Vector3.h"
#include "Vector4.h"
#include "Matrix3.h"
#include "quaternion.h"

namespace PBVP {
	/** Class encapsulating a standard 4x4 homogeneous matrix.
	@remarks
	OGRE uses column vectors when applying matrix multiplications,
	This means a vector is represented as a single column, 4-row
	matrix. This has the effect that the transformations implemented
	by the matrices happens right-to-left e.g. if vector V is to be
	transformed by M1 then M2 then M3, the calculation would be
	M3 * M2 * M1 * V. The order that matrices are concatenated is
	vital since matrix multiplication is not cummatative, i.e. you
	can get a different result if you concatenate in the wrong order.
	@par
	The use of column vectors and right-to-left ordering is the
	standard in most mathematical texts, and id the same as used in
	OpenGL. It is, however, the opposite of Direct3D, which has
	inexplicably chosen to differ from the accepted standard and uses
	row vectors and left-to-right matrix multiplication.
	@par
	OGRE deals with the differences between D3D and OpenGL etc.
	internally when operating through different render systems. OGRE
	users only need to conform to standard maths conventions, i.e.
	right-to-left matrix multiplication, (OGRE transposes matrices it
	passes to D3D to compensate).
	@par
	The generic form M * V which shows the layout of the matrix 
	entries is shown below:
	<pre>
	[ m[0][0]  m[0][1]  m[0][2]  m[0][3] ]   {x}
	| m[1][0]  m[1][1]  m[1][2]  m[1][3] | * {y}
	| m[2][0]  m[2][1]  m[2][2]  m[2][3] |   {z}
	[ m[3][0]  m[3][1]  m[3][2]  m[3][3] ]   {1}
	</pre>
	*/
	class Matrix4
	{
	protected:
		/// The matrix entries, indexed by [row][col].
		union {
			float m[4][4];
			float _m[16];
		};
	public:
		/** Default constructor.
		@note
		It initialize the matrix to identity matrix
		*/
		inline Matrix4()
		{
			m[0][0] = 1; m[0][1] = 0; m[0][2] = 0; m[0][3] = 0;
			m[1][0] = 0; m[1][1] = 1; m[1][2] = 0; m[1][3] = 0;
			m[2][0] = 0; m[2][1] = 0; m[2][2] = 1; m[2][3] = 0;
			m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
		}

		inline Matrix4(
			float m00, float m01, float m02, float m03,
			float m10, float m11, float m12, float m13,
			float m20, float m21, float m22, float m23,
			float m30, float m31, float m32, float m33 )
		{
			m[0][0] = m00;
			m[0][1] = m01;
			m[0][2] = m02;
			m[0][3] = m03;
			m[1][0] = m10;
			m[1][1] = m11;
			m[1][2] = m12;
			m[1][3] = m13;
			m[2][0] = m20;
			m[2][1] = m21;
			m[2][2] = m22;
			m[2][3] = m23;
			m[3][0] = m30;
			m[3][1] = m31;
			m[3][2] = m32;
			m[3][3] = m33;
		}

		/** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.
		*/

		inline Matrix4(const Matrix3& m3x3)
		{
			operator=(IDENTITY);
			operator=(m3x3);
		}

		/** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.
		*/

		inline Matrix4(const Quaternion& rot)
		{
			Matrix3 m3x3;
			rot.ToRotationMatrix(m3x3);
			operator=(IDENTITY);
			operator=(m3x3);
		}


		inline float* operator [] ( size_t iRow )
		{
			assert( iRow < 4 );
			return m[iRow];
		}

		inline const float *const operator [] ( size_t iRow ) const
		{
			assert( iRow < 4 );
			return m[iRow];
		}

		// OpenGL transformation matrix is column wise;
		void toOGLArray(float arry[16]) {
			Matrix4 mtx = this->transpose();
			for(int i = 0; i < 16; i++) {
				arry[i] = mtx._m[i];
			}
		}

		inline Matrix4 concatenate(const Matrix4 &m2) const
		{
			Matrix4 r;
			r.m[0][0] = m[0][0] * m2.m[0][0] + m[0][1] * m2.m[1][0] + m[0][2] * m2.m[2][0] + m[0][3] * m2.m[3][0];
			r.m[0][1] = m[0][0] * m2.m[0][1] + m[0][1] * m2.m[1][1] + m[0][2] * m2.m[2][1] + m[0][3] * m2.m[3][1];
			r.m[0][2] = m[0][0] * m2.m[0][2] + m[0][1] * m2.m[1][2] + m[0][2] * m2.m[2][2] + m[0][3] * m2.m[3][2];
			r.m[0][3] = m[0][0] * m2.m[0][3] + m[0][1] * m2.m[1][3] + m[0][2] * m2.m[2][3] + m[0][3] * m2.m[3][3];

			r.m[1][0] = m[1][0] * m2.m[0][0] + m[1][1] * m2.m[1][0] + m[1][2] * m2.m[2][0] + m[1][3] * m2.m[3][0];
			r.m[1][1] = m[1][0] * m2.m[0][1] + m[1][1] * m2.m[1][1] + m[1][2] * m2.m[2][1] + m[1][3] * m2.m[3][1];
			r.m[1][2] = m[1][0] * m2.m[0][2] + m[1][1] * m2.m[1][2] + m[1][2] * m2.m[2][2] + m[1][3] * m2.m[3][2];
			r.m[1][3] = m[1][0] * m2.m[0][3] + m[1][1] * m2.m[1][3] + m[1][2] * m2.m[2][3] + m[1][3] * m2.m[3][3];

			r.m[2][0] = m[2][0] * m2.m[0][0] + m[2][1] * m2.m[1][0] + m[2][2] * m2.m[2][0] + m[2][3] * m2.m[3][0];
			r.m[2][1] = m[2][0] * m2.m[0][1] + m[2][1] * m2.m[1][1] + m[2][2] * m2.m[2][1] + m[2][3] * m2.m[3][1];
			r.m[2][2] = m[2][0] * m2.m[0][2] + m[2][1] * m2.m[1][2] + m[2][2] * m2.m[2][2] + m[2][3] * m2.m[3][2];
			r.m[2][3] = m[2][0] * m2.m[0][3] + m[2][1] * m2.m[1][3] + m[2][2] * m2.m[2][3] + m[2][3] * m2.m[3][3];

			r.m[3][0] = m[3][0] * m2.m[0][0] + m[3][1] * m2.m[1][0] + m[3][2] * m2.m[2][0] + m[3][3] * m2.m[3][0];
			r.m[3][1] = m[3][0] * m2.m[0][1] + m[3][1] * m2.m[1][1] + m[3][2] * m2.m[2][1] + m[3][3] * m2.m[3][1];
			r.m[3][2] = m[3][0] * m2.m[0][2] + m[3][1] * m2.m[1][2] + m[3][2] * m2.m[2][2] + m[3][3] * m2.m[3][2];
			r.m[3][3] = m[3][0] * m2.m[0][3] + m[3][1] * m2.m[1][3] + m[3][2] * m2.m[2][3] + m[3][3] * m2.m[3][3];

			return r;
		}

		/** Matrix concatenation using '*'.
		*/
		inline Matrix4 operator * ( const Matrix4 &m2 ) const
		{
			return concatenate( m2 );
		}

		/** Vector transformation using '*'.
		@remarks
		Transforms the given 3-D vector by the matrix, projecting the 
		result back into <i>w</i> = 1.
		@note
		This means that the initial <i>w</i> is considered to be 1.0,
		and then all the tree elements of the resulting 3-D vector are
		divided by the resulting <i>w</i>.
		*/
		inline Vector3 operator * ( const Vector3 &v ) const
		{
			Vector3 r;

			float fInvW = 1.0 / ( m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] );

			r.x = ( m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] ) * fInvW;
			r.y = ( m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] ) * fInvW;
			r.z = ( m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] ) * fInvW;

			return r;
		}
		inline Vector4 operator * (const Vector4& v) const
		{
			return Vector4(
				m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w, 
				m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,
				m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,
				m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] * v.w
				);
		}

		/** Matrix addition.
		*/
		inline Matrix4 operator + ( const Matrix4 &m2 ) const
		{
			Matrix4 r;

			r.m[0][0] = m[0][0] + m2.m[0][0];
			r.m[0][1] = m[0][1] + m2.m[0][1];
			r.m[0][2] = m[0][2] + m2.m[0][2];
			r.m[0][3] = m[0][3] + m2.m[0][3];

			r.m[1][0] = m[1][0] + m2.m[1][0];
			r.m[1][1] = m[1][1] + m2.m[1][1];
			r.m[1][2] = m[1][2] + m2.m[1][2];
			r.m[1][3] = m[1][3] + m2.m[1][3];

			r.m[2][0] = m[2][0] + m2.m[2][0];
			r.m[2][1] = m[2][1] + m2.m[2][1];
			r.m[2][2] = m[2][2] + m2.m[2][2];
			r.m[2][3] = m[2][3] + m2.m[2][3];

			r.m[3][0] = m[3][0] + m2.m[3][0];
			r.m[3][1] = m[3][1] + m2.m[3][1];
			r.m[3][2] = m[3][2] + m2.m[3][2];
			r.m[3][3] = m[3][3] + m2.m[3][3];

			return r;
		}

		/** Matrix subtraction.
		*/
		inline Matrix4 operator - ( const Matrix4 &m2 ) const
		{
			Matrix4 r;
			r.m[0][0] = m[0][0] - m2.m[0][0];
			r.m[0][1] = m[0][1] - m2.m[0][1];
			r.m[0][2] = m[0][2] - m2.m[0][2];
			r.m[0][3] = m[0][3] - m2.m[0][3];

			r.m[1][0] = m[1][0] - m2.m[1][0];
			r.m[1][1] = m[1][1] - m2.m[1][1];
			r.m[1][2] = m[1][2] - m2.m[1][2];
			r.m[1][3] = m[1][3] - m2.m[1][3];

			r.m[2][0] = m[2][0] - m2.m[2][0];
			r.m[2][1] = m[2][1] - m2.m[2][1];
			r.m[2][2] = m[2][2] - m2.m[2][2];
			r.m[2][3] = m[2][3] - m2.m[2][3];

			r.m[3][0] = m[3][0] - m2.m[3][0];
			r.m[3][1] = m[3][1] - m2.m[3][1];
			r.m[3][2] = m[3][2] - m2.m[3][2];
			r.m[3][3] = m[3][3] - m2.m[3][3];

			return r;
		}

		/** Tests 2 matrices for equality.
		*/
		inline bool operator == ( const Matrix4& m2 ) const
		{
			if( 
				m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||
				m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||
				m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||
				m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )
				return false;
			return true;
		}

		/** Tests 2 matrices for inequality.
		*/
		inline bool operator != ( const Matrix4& m2 ) const
		{
			if( 
				m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||
				m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||
				m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||
				m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )
				return true;
			return false;
		}

		/** Assignment from 3x3 matrix.
		*/
		inline void operator = ( const Matrix3& mat3 )
		{
			m[0][0] = mat3.m[0][0]; m[0][1] = mat3.m[0][1]; m[0][2] = mat3.m[0][2];
			m[1][0] = mat3.m[1][0]; m[1][1] = mat3.m[1][1]; m[1][2] = mat3.m[1][2];
			m[2][0] = mat3.m[2][0]; m[2][1] = mat3.m[2][1]; m[2][2] = mat3.m[2][2];
		}

		inline Matrix4 transpose(void) const
		{
			return Matrix4(m[0][0], m[1][0], m[2][0], m[3][0],
				m[0][1], m[1][1], m[2][1], m[3][1],
				m[0][2], m[1][2], m[2][2], m[3][2],
				m[0][3], m[1][3], m[2][3], m[3][3]);
		}

		/*
		-----------------------------------------------------------------------
		Translation Transformation
		-----------------------------------------------------------------------
		*/
		/** Sets the translation transformation part of the matrix.
		*/
		inline void setTrans( const Vector3& v )
		{
			m[0][3] = v.x;
			m[1][3] = v.y;
			m[2][3] = v.z;
		}

		/** Extracts the translation transformation part of the matrix.
		*/
		inline Vector3 getTrans() const
		{
			return Vector3(m[0][3], m[1][3], m[2][3]);
		}


		/** Builds a translation matrix
		*/
		inline void makeTrans( const Vector3& v )
		{
			m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = v.x;
			m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = v.y;
			m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = v.z;
			m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;
		}

		inline void makeTrans( float tx, float ty, float tz )
		{
			m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = tx;
			m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = ty;
			m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = tz;
			m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;
		}

		/** Gets a translation matrix.
		*/
		inline static Matrix4 getTrans( const Vector3& v )
		{
			Matrix4 r;

			r.m[0][0] = 1.0; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = v.x;
			r.m[1][0] = 0.0; r.m[1][1] = 1.0; r.m[1][2] = 0.0; r.m[1][3] = v.y;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = 1.0; r.m[2][3] = v.z;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/** Gets a translation matrix - variation for not using a vector.
		*/
		inline static Matrix4 getTrans( float t_x, float t_y, float t_z )
		{
			Matrix4 r;

			r.m[0][0] = 1.0; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = t_x;
			r.m[1][0] = 0.0; r.m[1][1] = 1.0; r.m[1][2] = 0.0; r.m[1][3] = t_y;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = 1.0; r.m[2][3] = t_z;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/*
		-----------------------------------------------------------------------
		Scale Transformation
		-----------------------------------------------------------------------
		*/
		/** Sets the scale part of the matrix.
		*/
		inline void setScale( const Vector3& v )
		{
			m[0][0] = v.x;
			m[1][1] = v.y;
			m[2][2] = v.z;
		}

		/** Gets a scale matrix.
		*/
		inline static Matrix4 getScale( const Vector3& v )
		{
			Matrix4 r;
			r.m[0][0] = v.x; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = 0.0;
			r.m[1][0] = 0.0; r.m[1][1] = v.y; r.m[1][2] = 0.0; r.m[1][3] = 0.0;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = v.z; r.m[2][3] = 0.0;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/** Gets a scale matrix - variation for not using a vector.
		*/
		inline static Matrix4 getScale( float s_x, float s_y, float s_z )
		{
			Matrix4 r;
			r.m[0][0] = s_x; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = 0.0;
			r.m[1][0] = 0.0; r.m[1][1] = s_y; r.m[1][2] = 0.0; r.m[1][3] = 0.0;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = s_z; r.m[2][3] = 0.0;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/** Extracts the rotation / scaling part of the Matrix as a 3x3 matrix. 
		@param m3x3 Destination Matrix3
		*/
		inline void extract3x3Matrix(Matrix3& m3x3) const
		{
			m3x3.m[0][0] = m[0][0];
			m3x3.m[0][1] = m[0][1];
			m3x3.m[0][2] = m[0][2];
			m3x3.m[1][0] = m[1][0];
			m3x3.m[1][1] = m[1][1];
			m3x3.m[1][2] = m[1][2];
			m3x3.m[2][0] = m[2][0];
			m3x3.m[2][1] = m[2][1];
			m3x3.m[2][2] = m[2][2];

		}

		/** Determines if this matrix involves a scaling. */
		inline bool hasScale() const
		{
			// check magnitude of column vectors (==local axes)
			float t = m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0];
			if (!Math::floatEqual(t, 1.0, 1e-04))
				return true;
			t = m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1];
			if (!Math::floatEqual(t, 1.0, 1e-04))
				return true;
			t = m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2];
			if (!Math::floatEqual(t, 1.0, 1e-04))
				return true;

			return false;
		}

		/** Extracts the rotation / scaling part as a quaternion from the Matrix.
		*/
		inline Quaternion extractQuaternion() const
		{
			Matrix3 m3x3;
			extract3x3Matrix(m3x3);
			return Quaternion(m3x3);
		}

		static const Matrix4 ZERO;
		static const Matrix4 IDENTITY;
		/** Useful little matrix which takes 2D clipspace {-1, 1} to {0,1}
		and inverts the Y. */
		static const Matrix4 CLIPSPACE2DTOIMAGESPACE;

		inline Matrix4 operator*(float scalar) const
		{
			return Matrix4(
				scalar*m[0][0], scalar*m[0][1], scalar*m[0][2], scalar*m[0][3],
				scalar*m[1][0], scalar*m[1][1], scalar*m[1][2], scalar*m[1][3],
				scalar*m[2][0], scalar*m[2][1], scalar*m[2][2], scalar*m[2][3],
				scalar*m[3][0], scalar*m[3][1], scalar*m[3][2], scalar*m[3][3]);
		}

		/** Function for writing to a stream.
		*/
		inline friend std::ostream& operator <<
			( std::ostream& o, const Matrix4& m )
		{
			o << "Matrix4(";
			for (size_t i = 0; i < 4; ++i)
			{
				o << " row" << (unsigned)i << "{";
				for(size_t j = 0; j < 4; ++j)
				{
					o << m[i][j] << " ";
				}
				o << "}";
			}
			o << ")";
			return o;
		}

		Matrix4 adjoint() const;
		float determinant() const;
		Matrix4 inverse() const;

		/** Building a Matrix4 from orientation / scale / position.
		@remarks
		Transform is performed in the order scale, rotate, translation, i.e. translation is independent
		of orientation axes, scale does not affect size of translation, rotation and scaling are always
		centered on the origin.
		*/
		void makeTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation);

		/** Building an inverse Matrix4 from orientation / scale / position.
		@remarks
		As makeTransform except it build the inverse given the same data as makeTransform, so
		performing -translation, -rotate, 1/scale in that order.
		*/
		void makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation);

		/** Check whether or not the matrix is affine matrix.
		@remarks
		An affine matrix is a 4x4 matrix with row 3 equal to (0, 0, 0, 1),
		e.g. no projective coefficients.
		*/
		inline bool isAffine(void) const
		{
			return m[3][0] == 0 && m[3][1] == 0 && m[3][2] == 0 && m[3][3] == 1;
		}

		/** Returns the inverse of the affine matrix.
		@note
		The matrix must be an affine matrix. @see Matrix4::isAffine.
		*/
		Matrix4 inverseAffine(void) const;

		/** Concatenate two affine matrix.
		@note
		The matrices must be affine matrix. @see Matrix4::isAffine.
		*/
		inline Matrix4 concatenateAffine(const Matrix4 &m2) const
		{
			assert(isAffine() && m2.isAffine());

			return Matrix4(
				m[0][0] * m2.m[0][0] + m[0][1] * m2.m[1][0] + m[0][2] * m2.m[2][0],
				m[0][0] * m2.m[0][1] + m[0][1] * m2.m[1][1] + m[0][2] * m2.m[2][1],
				m[0][0] * m2.m[0][2] + m[0][1] * m2.m[1][2] + m[0][2] * m2.m[2][2],
				m[0][0] * m2.m[0][3] + m[0][1] * m2.m[1][3] + m[0][2] * m2.m[2][3] + m[0][3],

				m[1][0] * m2.m[0][0] + m[1][1] * m2.m[1][0] + m[1][2] * m2.m[2][0],
				m[1][0] * m2.m[0][1] + m[1][1] * m2.m[1][1] + m[1][2] * m2.m[2][1],
				m[1][0] * m2.m[0][2] + m[1][1] * m2.m[1][2] + m[1][2] * m2.m[2][2],
				m[1][0] * m2.m[0][3] + m[1][1] * m2.m[1][3] + m[1][2] * m2.m[2][3] + m[1][3],

				m[2][0] * m2.m[0][0] + m[2][1] * m2.m[1][0] + m[2][2] * m2.m[2][0],
				m[2][0] * m2.m[0][1] + m[2][1] * m2.m[1][1] + m[2][2] * m2.m[2][1],
				m[2][0] * m2.m[0][2] + m[2][1] * m2.m[1][2] + m[2][2] * m2.m[2][2],
				m[2][0] * m2.m[0][3] + m[2][1] * m2.m[1][3] + m[2][2] * m2.m[2][3] + m[2][3],

				0, 0, 0, 1);
		}

		/** 3-D Vector transformation specially for affine matrix.
		@remarks
		Transforms the given 3-D vector by the matrix, projecting the 
		result back into <i>w</i> = 1.
		@note
		The matrix must be an affine matrix. @see Matrix4::isAffine.
		*/
		inline Vector3 transformAffine(const Vector3& v) const
		{
			assert(isAffine());

			return Vector3(
				m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3], 
				m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3],
				m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3]);
		}

		/** 4-D Vector transformation specially for affine matrix.
		@note
		The matrix must be an affine matrix. @see Matrix4::isAffine.
		*/
		inline Vector4 transformAffine(const Vector4& v) const
		{
			assert(isAffine());

			return Vector4(
				m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w, 
				m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,
				m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,
				v.w);
		}
		
		static Matrix4 translateMatrix(const Vector3& vec); 
	};

	/* Removed from Vector4 and made a non-member here because otherwise
	OgreMatrix4.h and OgreVector4.h have to try to include and inline each 
	other, which frankly doesn't work ;)
	*/
	inline Vector4 operator * (const Vector4& v, const Matrix4& mat)
	{
		return Vector4(
			v.x*mat[0][0] + v.y*mat[1][0] + v.z*mat[2][0] + v.w*mat[3][0],
			v.x*mat[0][1] + v.y*mat[1][1] + v.z*mat[2][1] + v.w*mat[3][1],
			v.x*mat[0][2] + v.y*mat[1][2] + v.z*mat[2][2] + v.w*mat[3][2],
			v.x*mat[0][3] + v.y*mat[1][3] + v.z*mat[2][3] + v.w*mat[3][3]
		);
	}

}
#endif // __MATRIX4_H_INCL__
